To train young minds in rational philosophy - for the Philosophy Olympiad, and moreover for Life. My notes and discussions on various topics from Philosophy, Education, Astronomy, Physics & Programming as means to the above-stated end.

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May 10, 2010

What we call ‘laws’ are hypotheses or conjectures which always form a part of some larger system of theories and which therefore can never be tested in isolation.

Generally we speak of laws and theories as different forms of generalized scientific set of norms. Hypotheses and conjectures are considered to be propositions that aren’t a law yet. We get a general idea that all these are the components of a belief system. In science all these terminologies have different significance.

a)What is a Law?

A law is a set of generic notions that generally takes the form of a mathematical equation. Every component of a law has independent meaning and the structure of it gives relationship between them. Laws are universal in nature. They are proven from their derivation and thus are generally accepted to be true. This derivation process of the laws is the same to every formalism. Sometimes laws are derived from sets of observation; the direct implication of what is observed is considered to be true while sometimes observations are compressed and components of law are abstracted out. Laws originate in physics, mathematics, social science and even in psychology. On what grounds does one establish a law and the procedure of making it gives us the primary idea of how valid a law is.

b) What is theory?

Theory is understood to be a bigger set of laws; but a theory isn’t composed of random unconnected and independent laws about varied subjects. Theory pertains to one subject of enquiry and explains multiple phenomena not only by relating them to one another but also by providing common axioms supporting them. Theory comes from ‘theoria’ meaning perspective. A theory gives a perspective to its subject matter and rationalizes it. A theory is different from a law as a law will provide explanation ‘why’ and a theory will describe its other aspects completely.

c) What form does a law hold?

Laws state themselves in a similar way, like given a therefore b. A law by definition cannot be illuminating enough to give complete account of a and b. Also being a law doesn’t necessitate the fact that it works only in the provided cases. It is because a law is proved in a particular way, it is accepted by logic. When we consider a law to be correct we hold certain criteria for it. Law is a proposition as long as it isn’t proven. To be a proposition should be verifiable. Proven to true in many cases or all known cases it becomes a law. But such a law is thus naturally open to newer methods of verifiability. Thus law will no more hold the status of a true, rigid and consistent statement.

One can argue that law is the best possible explanation to what and how one sees nature to be. E.g. law of psychological consumption states that consumption is function of income. Here the law aims at giving the determinants of consumption that are influenced by income. Thus the proposed law is subject to individuals to be verified. It will stand in every case as long it works but still won’t entail consumption and its determinants; one counterevidence will disprove it, though many won’t prove it. Thus it becomes a hypothesis- proven proposition that hasn’t been disproven yet. Take Aristotle’s law of identity: a is a. It is a conjecture that is not disproven and is unproven but still considered to be correct. The semantic advantage in ‘a is a’ makes it a law.

d) Laws-a part of a larger belief system

Laws require a proof and proof implies scientific method. The foundations of our present understanding of science rest on axioms. We hold certain facts to be indubitable; they don’t have to be established methodically. But they themselves do not compose the laws.

There comes the relation of a law with its theory. Theories are constructed- they are representations of reality. They provide understanding of the world from a position; if x is explained by theory A and theory B of which theory A gives a wider perspective to understanding of all factors related to x then it is a better theory. The theory will speak about all angles about the given phenomenon. Laws are formulated about elements of a theory. E.g. law of gravitation is derived from the theory of gravity. Its mathematical side is abstract but the concept of gravity as explained in its theory is carried forward in the law as well. Thus the definition of gravity as given by the theory will set certain parameters for gravity to be expressed in and as certain terms; the law should equate gravity with all those factors to be consistent with the theory. Why is this required? Because a theory is based on axioms. These axioms are unquestioned and considered to be self-evident; they provide bases to the theory.

e) Sets of theories

If theories a, b and c rest on the same axioms, they shouldn’t be inconsistent with each other. The difference between theories a, b and c will be that their subject matter is different; thus they won’t be seen to be contradicting. But if state information about common issue or if the laws derived from them give different answers to the same question then there is inconsistence. Theory is not illogical construction on some basis; every proposition in a theory should be derived from the earlier. Deduction is the valid formalism in creating scientific theories. The logical necessity makes it necessary that every theory in a set, formed on the basis of common axioms, gives consistence among each other. Further if theory a is based on theories b and c, then they all lie in one set, there is consistency among them, theory a also may not follow directly from the axiom on which they rest but is not in contrast with it.

f) A law without its theory

Any law applied without its conditions will give untrue results. E.g. in the above example of the psychological law of consumption, one has to have an understanding of what ‘consumption’ means in the General theory of economics [that autonomous consumption isn’t a part of it]. If one ignores the natural conditions about testing the truth-value of laws, he will investigate about x and get an answer about x’, which will be a’ when a was expected by the law. E.g. if we want to test if only one line can pass through two points, then we must consider a plane in Euclidean geometry.

This seems to be compressed conditioning for someone who wants to learn what facts are, but how else have we developed knowledge in history? Man even when he thinks unbiased doesn’t store observe, understand and store every bit of reality he sees as his knowledge. It is out of his capacity. Forming representational knowledge is quite natural to him and works well to predict future when it can be determined. Having multiple sets of theories benefits our understanding; we can adopt that set which indefeasible and infallible.

It is because of its better set of axioms, that such a set will give realistic perspective of the world. So every implication of those theories will conjecture guesses about various subjects- these will be laws. Such laws will be unfalsified as long as their testing method doesn’t lie upon different set of axioms. This doesn’t mean that creating counter-examples can be restricted by such basic contradictions in axioms. One can build up such a counter-example and put every theory of a particular theory to test, e.g. a skepticist can establish hallucination as counterevidence to empiricism. But any theory based upon empiricistic axioms and consequentially the laws don’t stand to be disproved by an instance where perception is questioned [not questionable- as it is always possible to raise that point, but laws don’t follow directly from such basic axioms and have an independent logical structure apart from that].

Conclusion:

1- *Propositions in absence of counter-proof become hypotheses or conjectures. They are laws. They are deductively established from previous theories.

2- *Theories rest upon axioms and those having common axioms are a set giving a particular belief system.

3- *Laws cannot be separated from their previous theories and incidentally the axioms. They are verifiable but cannot be separated from a perspective that defines its components. Thus they should not be tested in isolation.